We will now introduce the Schramm-Loewner evolution (\(\mathrm {SLE}\) ). For more on \(\mathrm {SLE}\) , see e.g., [1]}, [2]}. Fix \(\kappa > 0\)  and for each \(z \in \mathbf {H}\)  let \(g_t(z)\)  denote the solution to
\(\partial _t g_t(z) = \frac{2}{g_t(z)-W_t}, \quad g_0(z)=z,\) 
